Angle subtended by common tangents of two ellipses $4{(\mathrm{x}-4)}^2+25{\mathrm{y}}^2=100$ and $4{(\mathrm{x}+1)}^2+{\mathrm{y}}^2=4$ at origin is 
 

Given ellipse

$$\begin{gathered} \frac{{(\mathrm{x}-4)}^2}{25}+\frac{{\mathrm{y}}^2}{4}=1 — ① \\ \frac{{(\mathrm{x}+1)}^2}{1}+\frac{{\mathrm{y}}^2}{4}=1 — ② \end{gathered}$$

equation of tangent of $①$ is 

$\mathrm{y}=\mathrm{m}(\mathrm{x}-4)\pm \sqrt{25{\mathrm{m}}^2+4}$

equation of Tangent of  $②$ is 

$\mathrm{y}=\mathrm{m}(\mathrm{x}+1)\pm \sqrt{{\mathrm{m}}^2+4}$

lines are subtended at origin is $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$